The role of large private sector firms in rerouting our food systems towards sustainability through climate-oriented innovation is highly contested. The contestation has resulted in a portrayal in academic literature of these incumbents as either the key driver of sustainability transitions or as fundamentally contradictory to addressing climate change in food systems. Controversies and tensions can reinforce stalemates, which hamper progress towards climate-oriented innovation. This study explores the utility of a paradox lens which shifts the research gaze to the emergence of unavoidable and persistent tensions in encounters of distinct logics and lines of action, and opens space to examine how these encounters can nevertheless be used productively and creatively in overcoming stalemates. Based on reflexive practice and interviews with professionals from seven purposefully selected incumbent private sector firms in the agri-food sector, we identify five paradoxes: the paradox of direction—between mitigation and adaptation; the paradox of justification—between exploration and exploitation; the paradox of internal alignment—between mainstreaming and specialization; the paradox of external alignment—between collaboration and competition; and the paradox of evidence—between accountability and learning. Our analysis of how agri-food firms navigate paradoxes focuses on considerations, tensions, and decisions in organizing climate-oriented innovation. In our discussion, we examine whether and how paradoxical thinking enables civil society practitioners to accelerate climate-oriented innovation in food systems through interactions and collaborations with the private sector. We conclude that a paradox lens affords researchers, practitioners, and policymakers to move beyond the binary view on the role of incumbents’ climate-oriented innovation, and instead provides strategic insights for engaging incumbents and their inherent contradictions in transforming our food systems under a changing climate.